Fuzzy rule-base driven orthogonal approximation

Abstract

In this study, orthogonal approximation concept is applied to fuzzy systems. We propose a new useful model adapted from the well-known Sugeno type fuzzy system. The proposed fuzzy model is a generalization of the zeroorder Sugeno fuzzy system model. Instead of linear functions in standard Sugeno model, we use nonlinear functions in the consequent part. The nonlinear functions are selected from a trigonometric orthogonal basis. Orthogonal function parameters are trained along with the Sugeno fuzzy system. The proposed model is demonstrated using three simulations-a nonlinear piecewise-continuous scalar function modeling and filtering, nonlinear dynamic system identification, and time series prediction. Finally some performance comparisons are carried out.

Representing Fuzzy Systems Universal Approximators

“…The aim of the paper is to prove that fuzzy systems are also universal approximators to continuous functions on compact domain in the case of the described subsystem inference representation corresponding to the fuzzy systems, as in the work of Kosko [11], Wang [16] and later Alci [1], Kim [10]. The paper is organized as follows: the first section provides a brief review on product sum fuzzy inference and introduces the concepts of additive and multiplicative decomposable systems; the second section presents a subsystem inference representation; the next sections discuss the cases of polynomial, sinusoidal, orthonormal and other designs of subsystem inferences; the last section presents some conclusions on the matter.…”

The Orthogonality between Complex Fuzzy Sets and Its Application to Signal Detection

“…(1) Orthogonality is also an important tool in traditional fuzzy systems. Orthogonal transformation method, orthogonal rule, and orthogonal approximation concept are frequently applied to fuzzy rule-based models [26][27][28], fuzzy neural networks [29,30], and fuzzy control [31,32]. Complex fuzzy sets as an extension of fuzzy sets have been studied.…”

A novel fuzzy c-regression model algorithm using a new error measure and particle swarm optimization

“…Fuzzy modeling is an effective tool for the approximation of uncertain systems on the basis of measured data (Hellendoorn and Driankov, 1997). The TakagiSugeno (T-S) model (Takagi and Sugeno, 1985) has been widely applied in many fields, such as modeling (Boukhris et al, 1999;Alci, 2008;Soltani et al, 2010a), control (Ying, 2000;Brdyś and Littler, 2002;Kościelny and Syfert, 2006;Qi and Brdys, 2009;Kluska, 2009) and fault tolerant control (Marx et al, 2007;Ichalal et al, 2010). In many studies, T-S based approaches such as the Gustafson-Kessel (GK) clustering algorithm (Gustafson and Kessel, 1979), the Gath-Geva (GG) algorithm (Gath and Geva, 1989), the fuzzy c-regression model clustering algorithm (Hathaway and Bezdek, 1993), enhanced fuzzy system models (Celikyilmaz and Burhan Turksen, 2008), the new FCRM clustering algorithm (NFCRMA) (Chaoshun et al, 2009; and the Fuzzy C-Means (FCM) clustering algorithm (Bezdek, 1981) are often used for the description of complex systems in a human intuitive way (especially the last one).…”